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Monday, July 4, 2011

A first without a second

For the Thomist, to say that God is the First Cause of things is, first and foremost, to say that He is the cause of their existence at every moment at which they do exist. God creates things out of nothing precisely in the act of conserving them in being, and apart from His continual causal action they would instantly be annihilated. You, the computer you are using right now, the floor under your feet, the coffee cup in your hand – for each and every one of these things, God is, you might say, “keeping it real” at every instant. Nor is this causal activity something anything else could either carry out or even play a role in. Creation – which for Aquinas means creation out of nothing – can be the act of God alone.

Where creation is concerned, then, God is “first” cause not in the sense of coming before the second, third, and fourth causes, but rather in the sense of being absolutely fundamental, that apart from which nothing could cause (because nothing could exist) at all. As serious students of the Five Ways know, the sorts of causal series Aquinas traces to God as First Cause are causal series ordered per se, not causal series ordered per accidens. In the former sort of series, every cause other than the first is instrumental, its causal power derived from the first. (See this post for more on the subject.) But where creation is concerned, Aquinas’s talk of intermediate or instrumental causes is only “for the sake of argument”; his point is that even if there were intermediate causes of the being of things, the series would have to terminate in a First Cause. In fact there is and can be only one Creator and He cannot in principle create through intermediaries. (That is not to say that God does not work through intermediaries in other respects. We’re only talking here about His act of causing the sheer existence of a thing or creating it out of nothing.)

Why not? Aquinas addresses the question at some length in the Summa Theologiae, the Summa Contra Gentiles, and De Potentia Dei. The arguments are difficult for someone not versed in the metaphysical presuppositions of Aquinas’s philosophical theology – indeed, some of them are difficult even for someone who is versed in the relevant metaphysics. But what follows will, I hope, suffice to convey some of the main ideas. (It will help considerably if the reader has at least some knowledge of such fundamental Aristotelian-Thomistic metaphysical notions as actuality and potentiality, form and matter, and the principle of proportionate causality; of the Thomistic arguments for the existence of God as pure actuality and as being itself rather than merely a being among others; and of the arguments for the uniqueness of anything that is pure actuality and being itself. This is all spelled out at length in chapters 2 and 3 of Aquinas.)

First, then, why does Aquinas hold that only God can possibly create out of nothing?

Here’s one way to understand it. Any of us can easily actualize the potential of the oxygen in the air around us to move, simply by waving our arms. Only someone with the relevant expert knowledge could take oxygen and hydrogen and synthesize water out of them. It would take greater power still to cause the prime matter underlying oxygen, hydrogen, or water to take on the substantial form of a tree. But creation out of nothing requires more power even than that, in fact unlimited power. For it is not a case of drawing out the potentialities that are already there in a thing, but rather causing a thing to exist entirely, together with its potentialities, where nothing at all had existed before. It isn’t a case merely of modifying what already exists, but rather of causing to exist in the first place that which all mere modification presupposes.

Limited causes are limited precisely by potentialities which are not actualized. Hence a sculptor is limited by the degree of skill he has so far acquired, by the limits on his dexterity given the structure of his hands, etc. He is limited also by the potentialities of his materials – their capacity to be molded using some tools but not others, their capacity to maintain whatever shape the sculptor puts into them, and so forth. Now that which creates out of nothing is not limited by any such external factors, precisely because it is not modifying anything that already exists outside of it. But neither can it be limited by any internal potentialities analogous to the limits on a sculptor’s skill. For it is not merely causing a being of this or that sort to exist (though it is doing that too) – modifying preexisting materials would suffice to cause that – but also making it the case that any being at all exists. And only that which is not a being among others but rather unlimited being – that which is pure actuality – can do that.

The idea is perhaps best stated in Platonic terms of the sort Aquinas uses (in an Aristotelianized form) in the Fourth Way. To be a tree or to be a stone is merely to participate in “treeness” or “stoneness.” But to be at all – which is the characteristic effect of an act of creation out of nothing – is to participate in Being Itself. Now the principle of proportionate causality tells us that whatever is in an effect must be in some way in its cause. And only that which just is Being Itself can, in this case, be a cause proportionate to the effect, since the effect is not merely to be a tree or to be a stone, but to be at all.

So only God – who just is pure actuality or Being Itself rather than a being among others – can cause a thing to exist ex nihilo. But why could He not work through instrumental causes in doing so? For all the preceding argument would seem to show is that Being Itself is the ultimate cause of any thing’s existing at all. That is, it suggests that any cause of a thing’s sheer existence that was less than Being Itself would, either directly or indirectly, owe its own existence to that which is Being Itself. But why couldn’t that which is Being Itself impart to other things their sheer existence through such an intermediary – through an instrumental cause which, like the effect, is merely a being among others rather than Being Itself?

Here’s one way to think about the problem with this idea. An instrumental cause causes by virtue of being used to alter what already exists, as a chisel is used by a sculptor to alter marble. But to cause the sheer existence of a thing ex nihilo is not to alter what already exists. In the case of a material thing, it does not involve causing already existing matter to take on a new form (as a sculptor does), but rather causing the matter and form together to exist. Hence while it makes sense to speak of using a chisel in the act of sculpting a statue out of marble, it makes no sense to speak of using a chisel in the act of causing a statue to exist ex nihilo. For before the statue was caused to exist ex nihilo, there was no marble on which the chisel could be brought to bear; and after the statue is caused to exist ex nihilo, there is nothing for the chisel to do, since the marble already is (by hypothesis) a statue. Now any purported instrumental cause involved in any act of creation ex nihilo would be like the chisel. It would be a fifth wheel – it wouldn’t be doing anything, and thus would not be causing anything, and thus would not really be an instrumental cause (because not a cause at all). Hence the very idea of God creating out of nothing through instrumental causes falls apart on analysis.

So, while popular images of God as First Cause have Him knocking down the first domino billions of years ago, and while even Aquinas might seem to make of Him the distant terminus of a regress of simultaneous currently operating causes, nothing could be further from the truth. God’s relationship to the world is in Aquinas’s view much more intimate than that, indeed, as intimate as possible. At least where the sheer existence of things is concerned, He and He alone is directly causing them at every instant. He is, as the Muslims say, “closer than the vein in your neck.”

Question 1: What about when God does form things out of pre-existing matter?

Please, PLEASE talk about "passive potency" and how that fits into Aquinas' philosophy of creation as expressed in this passage relating to the first human body:

"An effect may be said to pre-exist in the causal virtues of creatures, in two ways. First, both in active and in passive potentiality, so that not only can it be produced out of pre-existing matter, but also that some pre-existing creature can produce it. Secondly, in passive potentiality only; that is, that out of pre-existing matter it can be produced by God. In this sense, according to Augustine, the human body pre-existed in the previous work in their causal virtues."

He seems to be saying that only God can activate passive potency. I've searched fairly vigorously through his writings for clarification on what exactly passive potential is, but with no luck.

How would you define it?

Question 2: What about the "teleology" we observe in natural things? Doesn't that teleology also owe its existence to God at every instant? How then can it said to be inherent in natural things? Isn't it rather inherent in God - and given, at every instance, to natural things so that they partake of His mind just as they do of His being?

Recently I heard the argument advanced that God cannot be the First Cause because to be the First Cause hinges on their being an effect -- that is, until the first effect is caused, God would merely be the "First Cause in waiting." Thus, upon creating, God would actualize his potential to be the First Cause, which would be fatal to the argument.

Haven't you asked these questions before and gotten answers, if not from Ed, at least from some commenters here?

(1) In the passage you quote, Aquinas does not say that only God can activate passivate potential; the sentence immediately prior to the one you italicize, in fact, says exactly the opposite. All Aquinas is doing here is (in effect) answering the question, "In what ways can we say something is caused by creatures?" (That's the issue he's introducing in the first sentence of the passage.) And the two possible answers are (a) it can be caused by a created agent producing it out of matter, which is the same as to say that the created agent's active potential (=power to act so as to get the effect) activating something created that has passive potential (=power to be acted upon to get the effect); and (b) it can be caused by creatures in the sense that they provide the material (and thus the passive potential) but God, not a creature, activates it. That's all he's saying.

To say that only God can activate passivate potentiality would be to say that God is the only agent, the only active cause. Creatures can't be causes except by activating passive potentiality.

(2) I can't make heads or tails of your second question, and I doubt I'm the only one. The very existence of things at every instant owes itself to God and is also intrinsic to the things, so there is no inconsistency between saying that something is caused by God and intrinsic to things rather than God. If we were actually to insist that everything caused by God is intrinsic to God, we'd have to be pantheists, which there is excellent reason not to be. So why would we think that natural 'teleology' being created implies that it is intrinsic to God and not intrinsic to the natural things themselves?

Lefkis,

To be 'First Cause in waiting' in this sense God would have to be waiting in the first place, which presupposes that time and therefore motion already exist. Aquinas deals with this issue from the opposite direction (i.e., arguments that are more or less equivalent to saying that if God is First Cause His effects always have to have existed) at ST 1.46.1.

Brandon: "Haven't you asked these questions before and gotten answers, if not from Ed, at least from some commenters here?"

Bear with me, I can be a bit dense some times!

"active potential (=power to act so as to get the effect)... passive potential (=power to be acted upon to get the effect)"

Ah, it's becoming clearer! So the active potential has to do with the "activator" not the "activatee"?

I was understanding the passage to mean that some matter has both active and passive potential (and thus can be activated by creatures) while other matter had only passive potential (and thus could only be activated by God.)

Thanks for the clarification.

"If we were actually to insist that everything caused by God is intrinsic to God, we'd have to be pantheists"

Thanks for that. I guess my misunderstanding was a passage where Dr. Feser contrasts Platonic teleological realism with Aristotelian teleological realism in Teleology: A Shopper’s Guide:

"Platonic teleological realism holds that the irreducible teleology manifest in nature is extrinsic, entirely derivative from an outside source. Natural phenomena as such are not teleological, but they have been ordered to certain ends by (say) a divine mind... Aristotelian teleological realism holds that teleology or final causality is intrinsic to natural substances, and does not derive from any divine source."

In the light of the fifth way, if teleology is inherent to nature, then how can Aquinas argue that it requires a divine mind? It seems to me that Aquinas' view of teleology would have to be more Platonic than Aristotelian.

the argument cited by you is flawed since it supposes that always effect FOLLOWS cause temporally.

It grossly misunderstands St. Thomas cosmological arguments.

While that might be true in causes 'per accidens', i.e. your grandma giving birth to your mom is also the cause of your being born. In this kind of causation previous causation can stop with no effect on following causes (ie your grandmother dying will not undo your mother or you being born).

St. Thomas argues not regarding this kind of causes, but regardin causes 'per se' (which differ from causes per accidens), where cause and effect are simoultanous... ie if your hand moves a stick which moves a stone in turn, the movement, hence cause and effect, are simoultanous and if the hand ceases to move, the stick also stops and so the stone.

CREATION in St. Thomas sense is per se. It's not God pushing a button and starting the Big Bang and then leaving it be.

Creation is something that happens here an now, since if God would disappear all creation would disappear as well since God is sustaining the existence of all creation here and now, just like the hand moves the stick which moves the stone and if the hand stops the stick stops and stone stops.

Hence there is no 'following effect' not can there be a ' creation in waiting'

Creation is more than mere 'making out of nothing' for Classical THeism and St. Thomas, it's also sustaining the very existence what is created.

Creation is not a following effect from some kind of action that God did (like pushing the button of the Big Bang machine) but it is something that God *sustains* in His eternity, it's not te pelagian or deist conception of 'God creating at one point and then stopping' perhaps even leaving the universe on its own.

So even if there was NO Big Bang, and the universe always existed, St. Thomas argument would still be valid, as he does not assume that the universe had a start in his argument (even if of course he believed it did).

In conclusion the critique you reported does not even scratch Classical Theism, but does raise doubts on Deism and some modern forms of Theism for sure.

Does the distinction between causal series per se and per accidens hold on a B-theory of time? If the flow of time is an illusion and every moment is ontologically on par, then the notion of instrumental causes becomes problematic. Or does it? I have wondered about this for a while, but I can´t think it through. Could someone help?

“St. Thomas argues not regarding this kind of causes, but regardin causes 'per se' (which differ from causes per accidens), where cause and effect are simoultanous... ie if your hand moves a stick which moves a stone in turn, the movement, hence cause and effect, are simoultanous and if the hand ceases to move, the stick also stops and so the stone.”

If effect and cause are simultaneous then discriminating between them is a purely arbitrary or conventional matter as one is free to draw the border between the two wherever it suits him. The stone is moved by the stick is only one way to look at it. The other way could be, for example, to see the stonestick as one system where the movement or change in one can not be separated from the movement of the other part of the system. Also, both stone and stick and hand are connected and therefore influenced by infinity of other things and phenomena; all interconnected and mutually dependent. The whole universe is simultaneously involved in the movement of the stone and is at the same time influenced by stone’s movement.

Of course, one could argue that the movement of the hand that moves the stick and so on is caused by the intention of the man who holds the stick. Except that we don’t really know what intention is and how well is it insulated from other than itself things.

The notion of instrumental causes per se does not become problematic, because even a static four-dimensional block universe would be a compound of essence and existence which would depend for its being on that in which essence and existence are identical.

Now such a conception of the world -- which is really just a return to Parmenides -- is incompatible with an Aristotelian account of change, precisely because it amounts to the denial of real change. Though I would say that, rather than getting rid of real becoming altogether, it really just relocates it from the world to the mind -- on pain of an incoherent eliminativism -- and thus gives us a Cartesian-style dualistic view of the world, with all the problems of the other kind. But in that case it is like the moderns' attempted elimination of final causes by relocating all "directedness" into the mind -- it doesn't really get rid of the phenomenon the Aristotelian is talking about, but just moves it around.

Anyway, the four-dimensionalist view is IMO wrong in any case. This is among the subjects of my various current writing projects. More later.

"If effect and cause are simultaneous then discriminating between them is a purely arbitrary or conventional matter as one is free to draw the border between the two wherever it suits him. The stone is moved by the stick is only one way to look at it. "

It's not arbitrary at all because it depends on the nature and powers of the entities involved in the system.

Or better said: it depends on their degree of actuality and potentiality.

And actuality and potentiality are not symmetric. Actuality can exist even if there is no potentiality, but potentiality alone cannot exist, but it exists only in so far something is actual

That is, for a trivial example: the movements of the stone depends only on the fact that there is an actual stone that moves... The 'movement of the stone' in itself, is just a potentiality that by itself does not exist.

Moreover: To say that the stone moves the stick and the hand would be a logical fallacy (of confusing cause and effect… just by using common sense if we examine the system with physics alone leaving philosophy aside, it’s clear which is the mover and which the moved).

Since we know a stone cannot 'move by itself', nor can a stick, only the hand can be the 'first mover' in the series, and not the stone or the stick.

Also the hand could drop the stick and the stick and the stone would cease moving, but the hand wouldn't.

That is because the hand has greater actuality than the stick and the stone regarding kinetic movement and the stick and the stone have a lesser degree.

--

Another example:

When you see a locomotive pulling a set of wagons (on flat land not a slope) you think the wagons are moving the locomotive?

Here as well the locomotive has a higher degree of actuality, because of its engine, hence it can bring the potential of moving of the wagon in actuality.

The wagon, on the other hand has a lesser degree of actuality regarding kinetic movement: i.e. a wagon by itself can never push a locomotive, because the locomomotive has a motor, and a wagon has not

(unless some other power... on a slope a very heavy wagon COULD push a locomotive, because of gravity, here, however the system still isn't arbitrary… and we were in anyway discussing a train on flatland and not a slope).

Also, both stone and stick and hand are connected and therefore influenced by infinity of other things and phenomena; all interconnected and mutually dependent. The whole universe is simultaneously involved in the movement of the stone and is at the same time influenced by stone’s movement.

Of course, one could argue that the movement of the hand that moves the stick and so on is caused by the intention of the man who holds the stick. Except that we don’t really know what intention is and how well is it insulated from other than itself things.

Yes... but I never argued otherwise. Like I said there is an ASYMMETRY between actuality and potentiality.

The hand is influenced by the muscles, the muscles by chemical reactions and neuro-signals... and these on other events that regard atoms and then fundamental particles etc... that is true.

Same goes for the locomotive example: the locomotive actual power of movement depends on the motor of the locomotive, and this depends on the chemical reactions that cause the movement of the pistons, and these depend on molecules, and these on atoms and these on fundamental particles and forces, and so on…

The hand-stick-stone (or the locomotive) system is just a simplistic example to explain what a cause 'per se' is. No one is arguing the hand (or locomotive) is an absolute 'first mover' since it's not, obvioiusly.

In the end in this chain of causes per se there MUST be a terminator, otherwise nothing else would exist. If there where no atoms there would be no molecules, hence no neurons and muscle cells hence no hand.... and no stick and rock either….

… just like if we make the stick disappear the stone will not move anymore (but the hand will) or if we break the connection between two wagons, than some wagons will not move anymore, but the locomotive will)

----

Getting picky moment!

A physicist like myself (but even a decent highschool student who had basic Newtonian dynamics) might raise the question of ‘constant linear motion’.

In a perfect frictionless system, thus if we want to be extra picky in our examples, the stone and wagons will continue to move, HOWEVER they will not have the power to change their movement, i.e. they will move forward forever at the same speed and direction unless some other actual power changes their speed or course.

This would be true for Earth’s orbit as well: it depends ONLY on the Sun: if we take away the Sun the Earth will not have a circular orbit anymore, it will fly forever in one direction at constant speed.

That is because linear movement at constant speed is itself something actual at that point, actualized by the mover.

So we have again causes per accidens and per se: The movement of Earth itself might be per accidens (once moved in one direction it will move even without the Sun or whatever brought it to movement into the first place), but the orbit around the Sun is ‘per se’.

The same if the hand wanted to move the stone in a circular movement, or the locomotive wanted to take the train up a hill: the mover is necessary to ‘bring actuality to potentiality’.

You can thing many systems with causes per accidens or per se and some of these systems will have a combination of both causes (i.e.: like a car moving, uphill, against gravity if you wish: starting the motor is a cause per accidens, the motor moving the car uphill is a cause per se.)

In the cause per se the hand, stick and rock depend on the existence of atoms NOT vice-versa... it is NOT arbitrary, since atoms can exist even if no molecules exited or no hands or stick or stones.... but molecules, hands and sticks and stones can NOT exist if atoms did not exist.

Hence we se here also the asymmetry of actuality vs. potentiality.

Atoms have a certain degree of actuality and can realize the potentiality of making molecules (and these other stuff like a hand).

Molecules however would not even exist (much less a hand which is composed of different complex molecules) if there not be ACTUAL atoms which can realize the potential of forming molecules.After this HUGE premise regarding causes and potentiality and actuality we can return to Prof. Feser discourse: God is PURE ACTUALITY and the first cause.

Let’s look at ‘pure potentiality’. Pure potentiality is just NOTHING (and I mean NOTHING, not 'empty space', really nothing at all), since there is nothing actual (not even empty space which is after all something) there in the first place to have this potentiality, i.e. pure potentiality is not something in existence or that can even exist. It's not even a concept or idea since you need an actual intelligence to have concepts or ideas.

Also such nothing can never, by itself, become something: since to fulfill part of its potentiality it needs something actual, so something in existence.

So if there is creatio-ex-nihilo, i.e. from NOTHING, there must exist something that can truly realize something from this nothing at all is 'pure being', 'pure actuality' i.e. something that by itself is existence itself.

Also since creation, as we said, it's a cause per se, if such pure actuality would disappear, so would everything else.

Nothing happens instantly, except maybe gravity and we're not sure about that. But Feser's chain of causality certainly does not happen instantly. In fact, when we measure computer operations in nanoseconds and less, Feser's so-called instant chain is tediously slow. A medieval mind can be forgiven for this error. A modern mind should know better.

So there is a dubious difference between the "domino" version of First Cause and the Aquinas version.

But even if we ignore that and permit instant action, there's still no fundamental difference. There is merely a different point of view. At some point in the chain someone shouts "Stop!" They're sick of the ride. The infinite progression induces nausea. So that someone prays to "God" to get off the ride. But it's still an arbitrary stopping point.

In Philosophy of Mind Feser drags out the homunculus fallacy. I'll make use of it here. If the stick rolls the ball via the hand "actualizing" via the arm via the muscle, molecule, atom, etc..., the chain is simply embedding a smaller and smaller homunculus at each stage. Each stage has a little less of that "actualization" -- that magic "intent" to fulfill a "purpose" -- until "poof" we decide we must stop. What do we find there? Pure actuality -- that is, pure homunculus. But in this case instead of ridiculing the homunculus, Feser anoints it God. That's is the arbitrary nature of God and Feser's philosophy.

'Happening instantly' and 'causing at every instant' are not the same thing; they are as different as 'instantaneously' and 'simultaneously'. This is such an elementary distinction that people who cannot make it have nothing useful to say on the subject.

Nothing happens instantly, except maybe gravity and we're not sure about that. But Feser's chain of causality certainly does not happen instantly. In fact, when we measure computer operations in nanoseconds and less, Feser's so-called instant chain is tediously slow. A medieval mind can be forgiven for this error. A modern mind should know better.

Too bad it has nothing to do with 'happening insatantly'.

If you have an incredibly long train then there will be a delay between the locomotive starting and the last wagon moving, and so for the locomotive stopping and the last wagon stopping.

Still this does not change that it is the locomotive that causes the movement of the wagon in a cause per se.

So you 'objection' is fallacious.

Each stage has a little less of that "actualization" -- that magic "intent" to fulfill a "purpose" -- until "poof" we decide we must stop. What do we find there? Pure actuality -- that is, pure homunculus. But in this case instead of ridiculing the homunculus, Feser anoints it God. That's is the arbitrary nature of God and Feser's philosophy.

This is more a Straw-Man fallacy.

SOME chains do not need a terminator….

Also Thomas recognized this.

SOME chains, however, DO need a terminator, and especially some chain connected per se (either instantly or with a delay, whatever you prefer...).

Like a incredibly long train going uphill: you do not see the locomotive but you know it's there, since wagons cannot move against gravity since they have no motor.

Each stage has a little less of that "actualization"

To bad you got it backwards, the closer you go to the first cause the MORE actuality is present.

The locomotive has more actuality than the wagon... so to speak, because the locomotive does not need the wagon to move, but the wagon needs the locomotive to move.

Obviously in a chain per se there is a terminator which is pure actuality.

Your application of the homunculus fallacy here has really nothing to do with the subject.

At some point in the chain someone shouts "Stop!" They're sick of the ride. The infinite progression induces nausea. So that someone prays to "God" to get off the ride. But it's still an arbitrary stopping point.

The word arbitrary has been thrown around a lot here... I starting to doubt that people do not follow what Feser's writing or that they do not know what arbitrary means.

Since there is an asymmetry between actuality and potentiality, and since causal chains per se NEED a terminator, there is nothing arbitrary at stopping the chain at a being of "pure actuality", actually it's the only possible solution, since all others would be illogical.

--

The only arbitrary thing here is the way you take concepts and mash them together without properly understanding them...

Nothing happens instantly, except maybe gravity and we're not sure about that. But Feser's chain of causality certainly does not happen instantly. In fact, when we measure computer operations in nanoseconds and less, Feser's so-called instant chain is tediously slow. A medieval mind can be forgiven for this error. A modern mind should know better.

Too bad it has nothing to do with 'happening insatantly'.

If you have an incredibly long train then there will be a delay between the locomotive starting and the last wagon moving, and so for the locomotive stopping and the last wagon stopping.

Still this does not change that it is the locomotive that causes the movement of the wagon in a cause per se.

So you 'objection' is fallacious.

Each stage has a little less of that "actualization" -- that magic "intent" to fulfill a "purpose" -- until "poof" we decide we must stop. What do we find there? Pure actuality -- that is, pure homunculus. But in this case instead of ridiculing the homunculus, Feser anoints it God. That's is the arbitrary nature of God and Feser's philosophy.

This is more a Straw-Man fallacy... or at least you are making comparisons that make no sense.

SOME chains do not need a terminator…. Also Thomas recognized this. No one denies this.

SOME chains, however, DO need a terminator, and especially a causal chain connected per se (either instantly or with a delay, whatever you prefer... it matters not).

Like a incredibly long train going uphill: you do not see the locomotive but you know it's there, since wagons cannot move against gravity since they have no motor.

Each stage has a little less of that "actualization"

To bad you got it backwards, the closer you go to the first cause the MORE actuality is present.

The locomotive has more actuality than the wagon... so to speak, because the locomotive does not need the wagon to move, but the wagon needs the locomotive to move.

Obviously in a chain per se there is a terminator which is pure actuality.

Your application of the homunculus fallacy here has really nothing to do with the subject.

At some point in the chain someone shouts "Stop!" They're sick of the ride. The infinite progression induces nausea. So that someone prays to "God" to get off the ride. But it's still an arbitrary stopping point.

The word arbitrary has been thrown around a lot here... I starting to doubt that people do not follow what Feser's writing or that they do not know what arbitrary means.

Since there is an asymmetry between actuality and potentiality, and since causal chains per se NEED a terminator, there is nothing arbitrary at stopping the chain at a being of "pure actuality", actually it's the only possible solution, since all others would be illogical.

--

The only arbitrary thing here is the way you take concepts and mash them together without properly understanding them...

So from the perspective of B-theory, there really isn´t any objective change from potency to act, which means that the First Way is not going to work. But the Second Way (interpreted in terms of essence and existence) is still sound.

I suggest that you all stop arguing with Djindra. Its as pointless as playing Chess with someone who puts their captured pieces back onto the board and insists on moving his king around even after checkmate has occured.

"Still this does not change that it is the locomotive that causes the movement of the wagon in a cause per se."

-- yes, you're describing dominoes. So this is fundamentally the same as the "domino" version of arguments for First Cause.

"SOME chains do not need a terminator…"

That's begging the question. Chains always end in a particular perspective -- a perspective that simply gives up looking for the next link. But suppose I say "intentionality" in our brains needs no terminator?

"In the end in this chain of causes per se there MUST be a terminator, otherwise nothing else would exist."

That begs the question too. Obviously things do exist. And also, obviously, there is no one "chain." There are an infinite number of chains. That train "pushes" back. The ground "pushes" up. The sky "pushes" down. There is no end to it because eventually those "chains" wrap back the other direction.

"the closer you go to the first cause the MORE actuality is present."

So the atom has more actuality than a locomotive. How convenient for you!

"I suggest that you all stop arguing with Djindra. Its as pointless as playing Chess with someone who puts their captured pieces back onto the board and insists on moving his king around even after checkmate has occured."

You, or someone like-minded offered that advice before.

I indicated I would take it, and didn't. I should have.

Instead I added my own clutter to Feser's site by wasting time squabbling with a guy who says nominalism, of the parodic flatus vocis school no doubt, can be taken seriously, and easily defended.

"Where creation is concerned, then, God is “first” cause not in the sense of coming before the second, third, and fourth causes, but rather in the sense of being absolutely fundamental, that apart from which nothing could cause (because nothing could exist) at all."

This puts me in mind of something already alluded to in previous threads on the first two "ways": that both Gilson and Copleston took pains to point out that what was at issue there was not a horizontal series of causes which would be compatible with the postulate of the eternity of the world, but a hierarchical one.

And even further off the exact topic; one of what I now see as one of the most curiously interesting concepts I have come across in the area of scholastic metaphysics, is the idea of the "analogy of being". I could make no sense of that phrase at all in school, taking it to have some sense along the lines of "like being, but not being exactly".

Also been rereading Kneale and Kneale, somewhat more to my personal taste, and am reminded that anyone who imagines that the discussions of the Medieval logicians were sterile must have missed the passages wherein they point out how many modern logical developments were conceptually anticipated.

hello Ismael,It's not arbitrary at all because it depends on the nature and powers of the entities involved in the system. Or better said: it depends on their degree of actuality and potentiality.

I admit I know very little about Aristotle’s metaphysics and his idea of actuality and potentiality in particular. When a notion of different degrees of actuality and potentiality of different entities involved in the system is introduced I am not sure I understand. So please do explain how the stone and stick degree of actuality and potentiality differ. Is the degree of actuality (and potentiality) of stick greater or lesser than stone’s and why?

Also, again, why do I have to regard the entities involved in the system as hand, stick and stone and not for example as hand AND part of stick AND another part of stick AND last part of stick conjoined with a part of stone, AND the remaining part of stone? In other words not original three element system, but five element system? Or 75? There is infinity of ways to skin a cat.

… actuality and potentiality are not symmetric. Actuality can exist even if there is no potentiality, but potentiality alone cannot exist, but it exists only in so far something is actual. Well, I am not sure I understand it. Still, I don’t see how is it relevant to the observation I made in my previous letter.

That is, for a trivial example: the movements of the stone depends only on the fact that there is an actual stone that moves...

Excuse me, but are you saying that the movement of the stone depends on the movement of the stone??

The 'movement of the stone' in itself, is just a potentiality that by itself does not exist.

All depends what you mean by “exist”. There are limits to the application of the word. For example: does existence exists? Both asserting and denying leads to an absurd. But that is digression…

Otherwise nothing exists “by itself”. Every single thing, however big or tiny, concrete or abstract, material or mental, arises from and on the background of everything else. You can say that “Q” is a unique arrangement of everything that is “Not Q”.

“Exist in itself” is an incoherent notion. Which is not to say that nothing exists tout court, or that things are not real.

To say that the stone moves the stick and the hand would be a logical fallacy (of confusing cause and effect… just by using common sense if we examine the system with physics alone leaving philosophy aside, it’s clear which is the mover and which the moved).

I am afraid you are assuming something you are purporting to prove, I mean the difference between cause and effect. And appeal to a very stretchy and bendable idea of common sense without backing it up with something substantive is not helpful. And no, physics never deals with establishing the existence of cause and effect and even less with the difference about them. Physics is about discovering and describing regularities in nature starting from metaphysical assumptions. It doesn’t demonstrate the truth of these assumptions.For example any natural process can be time reversed (going from effect to cause instead vice versa) the whole universe could run “backward” in time and laws of physics would still be as valid and logically compelling as they are now.

Since we know a stone cannot 'move by itself', nor can a stick, only the hand can be the 'first mover' in the series, and not the stone or the stick.Also the hand could drop the stick and the stick and the stone would cease moving, but the hand wouldn't. I am sorry, but I can’t see how the hand only can be first mover any more than the stick or stone. A severed hand, or a dead man’s hand can’t move sticks or stones any more than it can move itself.

That is because the hand has greater actuality than the stick and the stone regarding kinetic movement and the stick and the stone have a lesser degree.

Please explain what do you mean by “greater actuality regarding kinetic movement”. Consider a rock flying through the air following the eruption of a volcano. Could you specify the causal per-se series arranged according to decreasing degree of “actuality regarding kinetic movement starting from the object possessing the greatest degree of that particular actuality and ending with the rock itself?

When you see a locomotive pulling a set of wagons (on flat land not a slope) you think the wagons are moving the locomotive?Your question can only make sense in a conventionally selected, limited and closed system of locomotive and wagon(s). Not at all different from hand-stick-stone system. So yes, I agree the locomotive pulls the wagons. But it is only because I assume you are asking within limits of a certain convention. But if I suspected you wanted to broaden the convention so it offers another look at the phenomenon of movement I could point out that the movement of locomotive is as much dependent on wagons (or their mass/inertia) as the movement of wagons on the pull of the locomotive. And everything is in a perfect Newtonian balance.

Here as well the locomotive has a higher degree of actuality, because of its engine, hence it can bring the potential of moving of the wagon in actuality.

But why do you stop at the engine? Why not stepping beyond it and include in your analysis the kinetic energy derived from combustion of diesel oil or coal or application of electromagnetic forces? And in the same vein why not going further and identify the factors that make the diesel oil, or electromagnetic field what they are? And, (I know it will sounds outrageous), since everything in the universe is interconnected in infinity of ways, how can we say that the inertia of the wagons does not partake in some way in combustibility of the diesel oil or the nature of the electromagnetic field? Please remember that I only remarked that in a process viewed from the position of the universal simultaneity of its elements there is no way to distinguish between cause and effect UNLESS we decide to look at it through the spectacles of a certain convention. Conventions are very powerful things and can be expanded infinitely, but they are never to be taken as something absolute. So again, if effect and cause are simultaneous then discriminating between them is a purely arbitrary or conventional matter as one is free to draw the border between the two wherever it suits him.

“ Like I said there is an ASYMMETRY between actuality and potentiality. “

Perhaps, but then you need to show its relevance to refutation of my, very simple, observation.

In the end in this chain of causes per se there MUST be a terminator, otherwise nothing else would exist. If there where no atoms there would be no molecules, hence no neurons and muscle cells hence no hand.... and no stick and rock either….

Again, you are assuming something and then proceed to the conclusion that this “something” MUST exist. That’s circular thinking. But that is not really important here. What is important is that you having a time-space snapshot of physical reality showing the infinite maze of interrelation

Again, you are assuming something and then proceed to the conclusion that this “something” MUST exist. That’s circular thinking. But that is not really important here. What is important is that you having a time-space snapshot of physical reality showing the infinite maze of interrelation of its elements CHOSE to “trace back” the chain of causes starting by the movement of the stone along a definite, but not only possible path. You looked for the first mover and chose a causal path that led you to a spot where you must (as you say ) conclude the existence of the first mover. The other thing is that your conclusion does not necessarily follow from your analysis which involves reduction to smaller, more elementary, “ingredients”. But the existence of atoms is no more elementary than the existence of a rock. Atoms obtain as result of man’s physical and, most importantly, intellectual manipulation of tangible object (sticks and rocks). No one has seen atoms, or quarks, or gravitrons. They are NOT ABSOLUTELY necessary. However their existence is accepted “conditionally”so long as they fit into the structure of matter proposed by science. They are convention that resulted from a particular way of understanding of and approach to material reality. But let’s for the sake of argument agree that rocks and sticks are “made of” atoms and atoms are made of paricles and particles are made of …My question is; why must we assume that the process of reduction to simpler more basic or deeper must stop somewhere and not continue forever? And let’s, again for the sake of argument, assume that the process does start somewhere and we arrive at the absolutely elementary indivisible thing. So what? Why such absolutely elementary “deepest” particle could not be a result of interaction of less elementary “less deep” particles we have already passed on our way “down”? Remember that in the per se arranged causal series all the elements are acting simultaneously on each other, so I am not restricted by the demand of temporal priority of one element over the other.As for the “getting picky” part of your letter I can’t see its relevance to our discussion, so I will only stop at it to point out that you are wrong saying:

“The movement of Earth itself might be per accidens (once moved in one direction it will move even without the Sun or whatever brought it to movement into the first place), but the orbit around the Sun is ‘per se’.

I admit I only a few hours ago acquainted myself with the concepts of per accidens and “per se” causal series, but I dare to think that you don’t fully understand the concept of “per se”causal construct if you think that movement (or rest) of the Earth, indeed its very existence may for even one instant escape it and be only a result of an accident occurring in the past. The third part of your letter repeats more or less what you have said before and what I have addressed.

Truth needs no qualifier. 2+2=4 is true because that's the way our universe works. Put two apples in a bucket, add two more, then count apples. That's what 2+2=4 means. It's true because we observe it's true. It requires no "universal." It's an empirical fact.

"Plus he has trouble understanding the difference between Plato's view of forms vs Aristotle."

I have no trouble understanding the difference. You demand I defend nominalism and when I do you whine. You whine because I countered the very arguments Feser has in TLS. If he makes them, I'm not going to ignore them. If he thought they were irrelevant he wouldn't have put them in his mythology.

"I suggest that you all stop arguing with Djindra. Its as pointless as playing Chess with someone who puts their captured pieces back onto the board and insists on moving his king around even after checkmate has occured."

No, I won't accept your dogmatic rules -- chess as played in Alice in Wonderland. That a terrible blow, I'm sure.

"What is important is that you having a time-space snapshot of physical reality showing the infinite maze of interrelation."

Exactly. Although I don't agree with your characterization of an atom as convention, if you mean by that an arbitrary convention, it's clear that the true believers here ignore the universe when they "discover" their supposed chain of causality. In fact, there is no chain. There is no First Cause. Every bit of the universe is interconnected. A more reasonable scenario is this: When I push on a mountain with a stick, half of the universe pushes with me and the other half pushes back. We cannot reduce this infinite web of cause and effect to one chain with one terminal link. It's not possible to find a terminal link.

"And, (I know it will sounds outrageous), since everything in the universe is interconnected in infinity of ways, how can we say that the inertia of the wagons does not partake in some way in combustibility of the diesel oil or the nature of the electromagnetic field?"

Are you suggesting diesel combusts differently if the locomotive is connected to a wagon (with its inertia)? Is there evidence for such?Would not introducing such speculation be against Occam's Razor?

In his book, TLS, Dr Feser does go back deeper in the example of the stone, stick and the hand. I think the example here is kept simple for illustration purposes, but then I'm not a philosopher :-).

Also, we know that the torque curve of diesel engine is influenced by the load: the greater the load the less flat the torque curve and the lesser the efficiency of the engine. And of course the smaller the load the flatter the curve…So inertia of the wagons does influence the performance of the locomotive engine...But that’s, of course, physics, not metaphysics.

Otherwise I am not sure Occam’s razor can be applied in metaphysics as rigorously as in science. If I am not mistaken Occam’s razor was very useful to, for example, D. Hume to amputate the formal and final causes from classic philosophy.

I borrowed the Last Superstition of E. Feser from a friend yesterday and spent greater part of the night to read it. Great fun until now. But I admit I mostly enjoy his passionate and quite witty demolishing of the New Atheist crowd. You know, unbearable jerks like Dawkins, Dennett, Hitchens…

And of course, like yourself, I am not philosopher, so it is not easy for me to form an opinion about the book. Well, I need to finish it first.CheersT. H.

djindra writes:"2+2=4 is true because that's the way our universe works. Put two apples in a bucket, add two more, then count apples. That's what 2+2=4 means. It's true because we observe it's true. It requires no "universal." It's an empirical fact."

This can't be true, since 2 and 4 are abstract objects. You don't "observe" them. You know them prior to observation. If truth requires no "qualifier," as you said earlier, then you don't need to put "two" in front of apples in order to know that 2 +2 + 4. You should be able to know it without an apple in sight. In fact, if someone told you that he had taken 2 apples and added another 2 apples and concluded that it was 5, you would not have to have observed the addition to know that it is wrong. In fact, it wouldn't matter if it were apples, ducks or moronic internet trolls who are philosophically clueless. It's always, everywhere wrong to claim that 2 +2 =5, even if you read in a history book that Aristotle Jones in 300 B. C. had claimed to have witnessed that 2 + 2 = 5. You don't even have to look at the evidence. Why? You already know that 2 + 2 = 4 is true because you have direct awareness of the abstract objects, numbers, of which this equation consists. That would make them necessary truths, by the way.

I should let you know Tom. djindra doesn't care about logic or the fact he is inconsistent. He doesn't care about facts, civility, reason, science, philosophy nor does he care if he makes a fool out of himself.

He's devolved into a pseudo Myers type of Gnu.

I think he is trying to provoke Prof Feser into getting banned or something? Maybe he is J? I just encounter J today on MandM's blog.

He's nuts.

What is it with these Gnu's? I seem to remember Chick Comic reading anti-Catholic fundies where more pleasant?

So if I add a liter of pure ethanol to a liter of water I will get a mixture with a volume of about 1.89 liters. I should, according to the djindra theory, conclude that 1 + 1 sometimes equals 1.89. Like TA said, this is checkmate mofo even though you probably don't even get it.

Are you a parent? Did your child arrive knowing 2 is an abstract object? I'll bet you didn't depend on that silly idea. You did what I did. You showed your child 1 finger, 2 fingers, 3 fingers, etc. Finally the abstract concept of numbers took root in the child based solely on observing these types of lessons. That's knowledge after the fact.

I would advise you guys to remember the Scholastic axiom "Cum negante principia nequit disputari": "With someone denying the principles, don't dispute." Treat them like the vegetable Aristotle said they would become...

Djindra's "reply" to TA is a rudimentary confusion. He confuses the process of acquiring mathematical beliefs with the underlying basis of mathematical truth. Only slightly less inept than arguing "I learned that electrons have a negative charge by reading about it in a physics textbook, therefore the reason electrons have a negative charge is because the physics textbook says so." "Checkmate!" yelled Djindra, as he slid his rook diagonally across the chessboard...

"He confuses the process of acquiring mathematical beliefs with the underlying basis of mathematical truth."

So tell me the difference in this particular case. Tell me how mathematical truth first arrived on the scene. People around here seem keenly interested in chains of this or that, so tell me where that first link of the mathematical chain of truth starts? Who first noticed 2+2=4 and how did the concept pop into the mind?

I guess you missed the fact that I'm doing it already. In The Last Superstition, page 43, Feser makes this assertion which is one reason nominalism is supposedly indefensible: "Mathematical truths in general are necessary and unalterable, while the material world and the human mind are contingent and changing." This is false. Mathematical truths are based on the behavior of the material world. If the material world is contingent, so are mathematical truths. So this particular swing against nominalism is foul.

What type of world could possibly exist where you add two things to two other things and get five?

Even if you had a world with some weird physics so that wherever 2 objects of one set where added to 2 objects in another and a 5th object spontaneously appeared you still would not have a world where 2+2=5.

You would have a world where (2+2)+1=5 but 2+2 would still objectively equal 4 not 5.

dinjra writes: "Are you a parent? Did your child arrive knowing 2 is an abstract object? I'll bet you didn't depend on that silly idea."

I can give one of two answers to this. First, I am not a parent, and thus I have no empirical basis to accept your argument. Second, apparently, according to your sense of things, if I were a parent, I would know. But such a hypothetical claim has no empirical referent. So, either way, you lose the argument.

However, let's take the second claim and employ it in a modus ponens:

If TA has children, he would know the nature of numbers.TA has childrenTherefore, TA knows the nature of numbers.

But that MP is a valid form of argument that is necessarily true. If not, then your argument against me doesn't work, since I can just claim that maybe next time it won't turn out to be valid.

But the fact is that more than one argument can have the property of validity at the same time, which means that validity is a universal property of any argument that exemplifies validity. Again, if not, I have no compelling ground to accept your "argument," since it has no characteristic that can justify your belief that it is valid. But if it does, that characteristic is true of every argument that is valid. And thus, we have a universal, necessary truth.

If your child who has five fingers tells you that he counted six, is he wrong in making that judgment? After all, he did the counting, and it seems to him that there are six fingers. If you say, child, you have only five fingers, he can, respond: "So, Daddy, is it true that anyone who says he has six fingers but only has five is always wrong in saying so?" "Yes." "But that means that it is necessarily the case that five is not six." "Oops!"

"Even if you had a world with some weird physics so that wherever 2 objects of one set where added to 2 objects in another and a 5th object spontaneously appeared you still would not have a world where 2+2=5."

Obviously false. Feser has many children and he seems to oppose an empirical basis of numbers. But I would hope any observant parent would notice how a baby's interaction with the world (often guided by adults) gives it all sorts of empirical truths that eventually (and sometimes quickly) take on the nature of absolute truth.

"I am not a parent, and thus I have no empirical basis to accept your argument."

You have no empirical basis to accept my example of how we come to this knowledge. It wasn't offered as a proof.

The question still remains, how do we come upon this notion that 2+2=4? I can think of no other way of knowing or even claiming this is true other than actually counting objects and discovering it is true. We did not pull that concept out of the thin air. And if tomorrow someone discovered a repeatable empirical case where 2+2=5, math would be forced to conform to the physical world, not the other way around. This forced conformity is, I think, even more certain than math and implies the physical world is the prime concern.

You say that given there is a world where two objects thrown in with two others result in five objects, "You would have a world where (2+2)+1=5 but 2+2 would still objectively equal 4 not 5."

This doesn't make sense but it's not our fault. We can't wrap our heads around the "weird physics" where 2 objects of one set added to 2 objects in another result in a 5th object appearing spontaneously. So even though this would be the objective truth in that weird world, from our point of view, 2+2 must still have an additional (+1) to equal 5. But we're trying to force our physics on that weird world. It may be that both 2+2=4 and 2+2=5 are equally true in that world. How would we know both cases were true? We'd count. We'd count both before addition and after. We'd make our new weird math conform to the physicality of the weird world. Math has no meaning without this conformity.

The Pythagorean theorem has meaning only because it describes relationships that conform to the way triangles measure-up in our vision of our world. The fact that the formula does seem to conform gives the formula its meaning, and it's why a solution was sought to begin with. We can plug in an infinite number of a, b and c and solve the equation, but none of those solutions would mean anything if the equation itself didn't express the relationship of sides in triangles. But notice that all solutions boil down to 0=0 which says nothing about triangles. We can create an infinite number of other, mathematically rule-correct, non-Pythagorean equations but all of them reduce down to 0=0. The famous e=mc**2 also boils down to 0=0. So does Einstein's equation mean the same as the Pythagorean theorem? No. Equations are not about the symmetry of 0=0 even though they all reduce to it. If all math merely represented this trivial meaning, math would be no more than abstract symbol manipulation. Math would be art. Numbers would be part of a math-artist's palette, nothing more. But math means something because it does not merely express 0=0. Einstein's equation means something because it expresses a fundamental relationship about our world. That's what math is. It's not about abstract numbers. Numbers are placeholders for objects or properties of objects. Math is ultimately about real objects and the relationships between them. If it wasn't about those real things I doubt math would have one practitioner and it would mean no more than a Pollock painting.

I never argued such a world is possible. Your ability to miss the point and change the argument in order to avoid the obvious is as strong as when you first started trolling here.

I used it to illustrate how it really isn't possible to have a world where 2+2=5 & that this mathematical truth is clearly not dependent on empiricism or the material world.

Because even in a hypothetical universe where addition objects appeared whenever addition took place doesn't render 2+2=5. It just means (+1) happens.

Thus it is clear Mathematics are both Universals and necessary truths.

You denial in the face of clear logic is just fundie Atheist Flat Eartherism.

Nothing more.

If we count we count 5 objects but that is only because 1+(2+2)=5 is a necessary truth. There is logically no such conceivable universe whose laws of physic dictate if there is no mandatory (+1) the result will still somehow be 5.

1+1=2, 2+2=4, (2+2)+1=5 are universals and necessary truths. Any hypothetical universe with a (+1) property is (A+B)+1=1+(A+B).

Respectfully, you should not talk about what you clearly do not understand. First that 2 + 2 equals 4 is a theorem of first-order PA. In fact, much much much less is needed, so that even an ultra-finitist like Edward Nelson has no problem with this statement. You could retort, "But how do you know those axioms are true?" I will make two points -- which are rather banal, actually, but then your argument is also a banal version of nominalism, and what is worse, trivially wrong. First, our conception of numbers is informed by our experiences. We sense things, we notice patterns and from there we conceive these abstract thingumajigs that obey such and such properties. And from these properties it follows that 2 + 2 = 4.

Now let us suppose that a universe where 2 + 2 = 5 and hold intelligent creatures could exist; it cannot, because it would mean that things would pop into being out of nothing, but let us grant its reality for the sake of argument. Now, these rational creatures would conceive a brand of arithmetic where 2 + 2 equals 5. The years pass, and some mathematical genius, possibly crazy, invents these numbers obeying the first-order Peano axioms. People would look at it, probably shrug their shoulders and say, "in our universe 2 + 2 = 5 so while your work shows admirable creativity it is hardly interesting, because it fails to capture how our universe works." To put my little fable in other words, if you could conceive a non-contradictory arithmetic where 2 + 2 = 5 (which you cannot, in any reasonable way) the numbers would not be what we call "Numbers" but something else entirely. Still in other words, changing names does not automagically change the nature of what those names refer to.

Mathematics may have arisen as a commentary on that common field of experience we usually call reality, but very early in its history it has shed off those shabby trappings. Its object of study is what we could call, lacking a better word, and with no implied adherence to any version of platonism, the mathematical universe. Contrary to what you state, Mathematics is *not* "ultimately about real objects and the relationships between them". At the root of this confusion is the failure to recognize the autonomous reality of Mathematics. Mathematics is an independent discipline and does not need the validation of physics, biology or whatever empirical science to justify its existence. This is not an opinion but a matter of *fact*. You can disagree all you want, it is absolutely irrelevant. It is mathematicians that decide the course of Mathematics, and while many do Mathematics motivated by real world problems, equally many do not give a hoot about whether any connection of their work with the "real world" can be made.

"I used it to illustrate how it really isn't possible to have a world where 2+2=5 & that this mathematical truth is clearly not dependent on empiricism or the material world."

Your illustration missed my point. Math is meaningless unless it's about the real universe at our fingertips. It is clearly dependent on the real world for its meaning. Even when mathematicians strike out in esoteric adventures they are working from a foundation that assumes math means something; and I think it's obvious that that meaning is at the root inseparable from the real world. IOW, math owns its very meaning to the empirical. If you separate numbers from the real world they cease to have meaning, like if you separated "apple" from apples the word would cease to have meaning. So your free-floating abstractions have no meaning and they abstract nothing.

That's the point.

"If we count we count 5 objects but that is only because 1+(2+2)=5 is a necessary truth."

I say there is no such thing as a necessary truth therefore that statement is vague to me. What in your mind distinguishes necessary truth from plain truth?

"You have blind mindless faith radical nominalism is true. But no rational reasons for it."

I do have faith, reasonable, I think, that the universe exists and there is no meaning and no existence outside it. Those who have faith in mystical "abstractions" rooted nowhere in material substances have an unreasonable faith since they have no evidence that the non-material realm exists.

Existence of people who may do math and not give a hoot about any connection of their work with the "real world" is not the question. The ultimate questions are, would that work mean anything? Would that work have any relevance at all? Would the symbols they use have any meaning? Would those symbols abstract or generalize from something or to anything? If they do not, "abstraction" become nonsensical, the symbols become mere squiggles on paper, and the whole enterprise becomes nonsense art.

I realize there are some hard-core "platonist" mathematicians. But I respectfully disagree with them.

>I do have faith, reasonable, I think, that the universe exists and there is no meaning and no existence outside it.

You have a mindless belief but clearly it is not reasoned out. I mean 2+2=4 is not a necessary truth?How is that not the same as believing in FSM or Elves?

>Those who have faith in mystical "abstractions" rooted nowhere in material substances have an unreasonable faith since they have no evidence that the non-material realm exists.

I don't believe in extreme strong realism either. Plato is wrong. Moderate realism OTOH is clearly the simple approach and correct view. You view is mindless esoteric irrational mysticism. You are just not rational.

First, for the purposes of what I said it is completely irrelevant if one is platonist, a formalist, a constructivist or whatever ist one cares to consider. Second, the meaning of a mathematical work is to be found within the ordered totality of mathematics itself, not in other disciplines. Claiming otherwise is to subordinate mathematics to externally derived standards, to make it a parasite of other disciplines and deny its autonomy. This goes completely against the facts and experience of mathematics. Third, whether or not you think this makes mathematics a nonsensical abstraction is not only completely irrelevant but betrays both a profound misunderstanding of mathematics as well as a misunderstanding and even ignorance, of the history of its relations with other disciplines, most notably physics. Fourth, relevance is judged by *mathematical* standards, not by the standards of physics or biology or whatever modern empirical science you care to name. Fifth, contrary to what you say the fact that many, I would bet even the vast majority, of mathematicians do their work happily ignoring whatever real-world connections may exist is relevant, because it shows clearly that while connections to other disciplines are a fruitful source of mathematics, these are not essential to its fundamental nature. Discovering these connections is not the work of a mathematician *qua* mathematician, but of physicists, economists, etc. Sixth, whether you disagree with some, many or all mathematicians is irrelevant; mathematicians will continue with their enterprise nonetheless, which like any scholarly pursuit, is simply the understanding of the object of their study. Nothing more, nothing less.

"Claiming otherwise is to subordinate mathematics to externally derived standards, to make it a parasite of other disciplines and deny its autonomy."

Well, I do deny its autonomy. It does not exist in a vacuum. It has no meaning within a vacuum. To claim that it does is to profoundly misunderstand meaning itself. Because what you're really saying is that something like "Colorless green ideas sleep furiously" has meaning simply because it follows a syntactical order that you create out of nothing. IOW, you're claiming that syntax is semantic. And whether you intend to or not, you're contradicting one of Feser's pet projects -- that minds need more than syntax to find meaning.

1. You really do not get it, do you? You can deny all you want, it is irrelevant because mathematics *is* autonomous. I am describing a *state of affairs*, not spouting an ill-informed opinion based on some fuzzy, ignorant, half-assed notion about what mathematics is supposed to be.

You think this state of affairs is wrong? Feel free to lobby to constrain and censure the mathematical output to accord to party-approved standards. Any mathematician will tell you what the result will be: a fatal impoverishment of mathematics, with disastrous consequences not only for teaching but for all the disciplines that depend on mathematical research. If you had the faintest inkling of the intense relationship between mathematics and physics say, you would understand what I am saying.

2. I am *not* claiming anything of the sort you say I am. Everyone with even the most cursory knowledge of logic knows the difference between syntax and semantics. Such a person also knows that the relation between them, in mathematics, runs very deep. This is the subject of Big Theorems, starting with Goedel's completeness theorem (not to be confused with the incompleteness theorems).

It is *you* who do not understand what I meant by "the meaning of a mathematical work is to be found within the ordered totality of mathematics itself" and everything else related, and project on me formalist tendencies that I adamantly reject.

3. There is absolutely no contradiction between my claims and the claims of prof. Edward Feser, partly because what I claim is a banality that is only denied by a confused, wrong-headed, ignorant bluff that insists that every type of knowledge bows down and subordinates to his Empirical Idol.

That in your own mind meaning in mathematics can only be found in the empirical disciplines, or otherwise it devolves in meaningless syntax, says nothing about mathematics, but it does reveal something about your own mind.

4. Mathematics does not exist in a vacuum, this is perfectly correct. Mathematics could be said to be an art that we know how to use and as such it is part and parcel of the totality of human culture. But this does not mean what you think it does.

5. Is your arrogance to the point that you think you know better than mathematicians about the nature of mathematics? I am not a very patient men, so let me end up this as bluntly as possible: you do not know and you do not understand mathematics. Your opinion is about as informed and relevant as the moo that a cow makes.

Djindra, July 10 1154:I say there is no such thing as a necessary truth therefore that statement is vague to me ... I do have faith, reasonable, I think, that the universe exists and there is no meaning and no existence outside it. Those who have faith in mystical "abstractions" rooted nowhere in material substances have an unreasonable faith since they have no evidence that the non-material realm exists.

How can such an empiricist hold that there is no such thing as a necessary truth? This is the only world we can measure and observe, so anything true is true in this (ie, all) world(s).

Because to believe in possible alternatives "rooted nowhere in material substances" would be to have "an unreasonable faith" in theory over practical experience - far from the empirical evidence demanded of others.

"Mathematics could be said to be an art that we know how to use and as such it is part and parcel of the totality of human culture."

Hopscotch has rules, has a type of internal consistency, we know how to use it to have fun, and is part of human culture. But a nominalist need not worry about Hopscotch being a stumbling block. Your description of your trivial mathematics poses no more of a problem than hopscotch.

Djindra:You must assume that I think our universe or one universe is necessary. I don't. It simply is.

I'm not assuming anything. Just asking you what you always demand of others: where is the evidence "rooted ... in material substances" that I can observe to give me empirical proof our universe isn't necessary, or simply is?

If you've reached your conclusion by some other means than physical observation then, by your own words, it seems that your belief in a universe that "simply is" shows that you have faith in mystical "abstractions" rooted nowhere in material substances. Given you typically dismiss everything you claim follows from such faiths, I take it you would have us dismiss your comments?

"If you've reached your conclusion by some other means than physical observation then, by your own words, it seems that your belief in a universe that 'simply is' shows that you have faith in mystical "abstractions" rooted nowhere in material substances."

Do you doubt the existence of the universe? Is this a mystical belief? Your definition of mystical makes the word meaningless. We might as well delete it from the dictionary.

You have not met a single one of my arguments or claims (I sincerely doubt you even understand them) and keep trotting out the same idiotic line of "meaningless mathematics" or a nominalism that I have already stated I reject. By all means, do not let facts, those irritable little buggers, get in the way of your beliefs.

Oh, just one more comment and I am through with you. The irony with your post is that while as I have already said, I am wary of formalism, a sizeable portion of the mathematical community tends to lean to the formalist camp. So why don't you get up and take your private little war to them?

Djindra:Do you doubt the existence of the universe? Is this a mystical belief? Your definition of mystical makes the word meaningless.

You're arguing with yourself. This is not my definition of mystical, but yours that you describe as meaningless.

I refer you again to your comment on July 10 where you wrote: Those who have faith in mystical "abstractions" rooted nowhere in material substances have an unreasonable faith since they have no evidence that the non-material realm exists.

Read what you wrote very carefully. By 'evidence' you can't mean something material unless you're asking for material evidence of the immaterial which, frankly, wouldn't surprise me of you. But you also can't mean anything but material here or else the statement is obviously false. (The evidence might not persuade you but that's irrelevant to your statement).

To me it seems tricky to make sense of exactly what you are saying; so instead I ask, "What is your evidence rooted somewhere in material substances for the claim that our universe isn't necessary, it simply is?" I'm not questioning its existence but how you know it's contingent, and not necessary.

But you don't answer my question. You choose to attack a straw man. Perhaps because that is easier than admitting your metaphysical commitment to a contingent universe is to admit some other possible existing or non-existing universe, and this isn't rooted in any material observation. And that by your own (admittedly very strange) lights amounts to something mystical instead of a (quite possibly well reasoned) metaphysical conclusion.

"You have not met a single one of my arguments or claims (I sincerely doubt you even understand them)"

Right back at ya.

This topic came up because mathematical "truths" are supposedly necessary and unalterable, and this somehow poses a problem for nominalists. Yet nothing you've said poses a problem. For example, your version of math semantics is supposedly self-contained within math itself. I'll draw a parallel to the self-contained semantics of computer languages. There are different syntaxes for "while" loops in various languages, but programmers must understand the semantics of looping itself. This semantic "truth" is a function of the formal specification of the language and the fact that looping is usually required in the "art" of programming. But this formal application of the word "semantics" is not the semantics I mean and is not the sort of semantics that has any sort of truth value outside the programming environment. I can write a program that is total nonsense -- it does nothing "true" or "false" -- yet has perfect syntax and makes use of the semantics of the language. Any other programmer could follow my logic. It would be "true" in that regard. My program might even be arbitrarily interpreted as a "proof" that looping works within looping. But this program would have no truth value outside that narrow focus. This is how you are presenting your math_in_isolation. And since it has no need for truth outside of its isolated environment, it's truths are certainly not necessary. They may be totally arbitrary. In fact, I doubt we have a way of knowing one way or the other. Its findings are likely contingent because the axioms and rules are likely an invention of the human brain. So this math poses no problem for nominalism -- not that the other math did either.

It is bad form to quote from one's own words, but I hope you will excuse me. From post July 10, 2011 1:38 PM:

"First, for the purposes of what I said it is completely irrelevant if one is platonist, a formalist, a constructivist or whatever ist one cares to consider."

Read it again. If I mentioned nominalism in my subsequent posts is because you keep projecting on me nominalist or formalist tendencies which I either reject, or as far as I can understand, look down on them as very suspicious. Read my posts again; I never claimed that the concept of necessary truths is problematic for nominalists; it is a relevant question but orthogonal to what I claimed. You consistently misunderstood what I said (but then again, I probably have a share in the guilt).

For the umpteenth time, it is not "my version of math semantics". I described a state of affairs. Mathematics is autonomous, and whatever you intend by "meaning" that you so desperately want to find in mathematics is either not there, or if it is, it is to be found in the ordered totality of mathematics. Feel free to not believe me -- I am the first to admit that I am nobody of relevance and my opinion counts very little (but contrary to yours, it is actually informed). Go ask the mathematicians; Take a survey; browse the peer-reviewed mathematical journals; browse the arxiv (the math section publishes several hundreds of preprints a week). Pick up a decent mathematics book and read it through.

To respond to your programming language analogy I would have to disentagle the chaff from the wheat; mention things like the Curry-Howard isomorphism (roughly, proofs and programs are the same thing and, to pursue your analogy, it is very easy to program a computer to churn out mathematical truths -- a supremely uninteresting and irrelevant task, by the way); to point out the several equivocations you make or the misreadings of what I actually claimed. But I won't because it would be a waste of time. Instead, to actually have any chance, however slight, of progressing and clearing out any possible misunderstandings between us, let me make you a simple question:

Let us consider Euclidean geometry. It first arose because of very practical needs, but already in Euclid's elements' book, arguably the most important book in the history of mathematics, whatever connection to the actual world there is is blissfully ignored. Let us imagine that we lived in a universe where Euclidean geometry had absolutely no relevance whatsoever to our empirical theories. How would you characterize a mathematical work expounding it (e.g. a version of Euclid's elements)? Is it "meaningful"? If not, why so? Is it "relevant"? If not, why so?

Djindra: I do have faith, reasonable, I think, that the universe exists and there is no meaning and no existence outside it (2)

Djindra: You must assume that I think our universe or one universe is necessary. I don't. It simply is. (3)

Djindra: There is no proof it is necessary or not. And I don't claim to know. I don't draw any conclusions from this ignorance. (4)

Thank you for that clarification (I think!). To me, your statement (3) is materially different from saying "I do not know whether this universe is necessary or not."

I have to ask, therefore, of your statement (1): did you mean to say, "I do not know if there are such things as necessary truths?"

Because if (1) stands, I still have a problem: it doesn't appear to be a statement about physics or matter so how did you evaluate its truth empirically?

Also, given that there are no empirical observations you can make to determine the truth of your statement (2), ie, that the faith expressed there is "rooted nowhere in material substances", could you explain what makes your faith in this case "reasonable"?

Djindra: However, if someone claims to have a necessary truth, I think it's clear that that person should have to explain exactly what he means by "necessary" and why his truth fits that meaning.

Ben Yachov and others have done exactly that in their earlier comments. And you're arguing with a bunch of Aristotlean-Thomists: would it be so hard to use the compute power at your fingertips to find out what, say, Aristotle means by necessarily true?

The point I really wanted to make is: your statement (1) is a metaphysical proposition. How does an empiricist like you, supposedly requiring that truths be "rooted ... in material substances", determine whether (1) is true or not? You say: "It is possible that 2+2=5 is true somewhere but we can't wrap our heads around the 'weird physics' of such a world" - ok, how do you know this is true? Where did you physically observe this fact that 2+2=4 isn't necessarily so?

Because if you believe all that strangeness (and, let's face it, you argue as if you do) no empirical judgement has informed that belief. And I'm not sure where that leaves an empiricist/nominalist/whateverist like you, but it certainly isn't persuasive to those without a prior commitment to utter horseshizzle.

Djindra: Truth needs no qualifier. 2+2=4 is true because that's the way our universe works. Put two apples in a bucket, add two more, then count apples. That's what 2+2=4 means. It's true because we observe it's true. It requires no "universal." It's an empirical fact.

Understanding that you have a problem with universals I imagine you have a problem with the series of numbers being infinite? But you should agree that there are only finitely many material things. So what happens, in your view, when you take the number of all material things and add 1 to it, or multiply it by 2?

I'm glad you brought up Euclid's geometry. How do you know his first postulates are true? What makes them self-evident? We both know the fifth postulate was considered not so self-evident. But what makes anything self-evident? Plato's Socrates famously "proved" this self-evident knowledge was due to innate knowledge "remembered" from past lives. I think we can dismiss that. So what is left?

"Also, given that there are no empirical observations you can make to determine the truth of your statement (2), ie, that the faith expressed there is 'rooted nowhere in material substances', could you explain what makes your faith in this case 'reasonable'?"

I can easily observe that disputes that are not based in the material world lead nowhere. They never end. The differences of opinion diverge, they don't seem to ever converge. IOW, they end up as meaningless if meaning is supposed to have some sort of truth-value.

Your questions have at best only a tangential relevance to my claims, which just reinforces my suspicion that either one of us (or both) is misunderstanding the other. So, would you please answer my questions in my last post? Otherwise, there is a real possibility that we will keep moving in circles, instead of spiraling towards the truth.

Don Jindra:I can easily observe that disputes that are not based in the material world lead nowhere. They never end. The differences of opinion diverge, they don't seem to ever converge. IOW, they end up as meaningless if meaning is supposed to have some sort of truth-value.

And here too, you'd be wrong by your OWN standards. For example, I can easily observe that:

(2) A formal proof to the theory of Pierre de Fermat's that no +ve integers a, b, and c can satisfy the the equation a^n + b^n = c^n for any integer value of n greater than two had been the subject of centuries of dispute till 1993.

These are just two "disputes that are not based in the material world" (to use your rather loose phrasing) that did not "lead nowhere".

Note that I didn't even dispute your question-begging assertion that disputes with diverging differences of opinion find their truth-values from consensus, or convergence between the disputing parties. Nor have I adduced "disputes that are ... based in the material world" where differences of opinion have not converged (eg. Global warming/climate change/climate disruption, and Darwin's theory of evolution among many). Your own words demonstrate your confirmation bias and refute you.

I would also note, as an aside, that in the past you've been quick to impute intellectual dishonesty to your host here, Professor Feser. Yet you ignore questions that you can't answer, make bald assertions about all sorts of propositions where if you were consistent you would have to say "I do not know about x as I have no material evidence for it." If C S Lewis, say, shared your lack of integrity, then I can imagine his debate with Anscombe would have gone the way all disputes with you seem to.

I'd love to know your answers to my questions though I also think that you and I have stunk up the joint enough. I'd love for you to have access to all the tools of philosophy to make your case. But, given that you reject them, I say your position can't be defended on its own terms obviously.

"I never claimed that the concept of necessary truths is problematic for nominalists;"

It may be unfair to you but there is a reason I keep coming back to nominalism vs realism. That was the topic. It spilled over from another thread. So my differences are not with you only. I tend to write responses in a general fashion knowing others might jump in. Again, I know this will not always be fair to you.

"it is not 'my version of math semantics'. I described a state of affairs."

We have a different take on the state of affairs. Maybe we have a different take on 'meaning' too. But I do suspect most mathematicians think their work means something -- even if only to themselves -- otherwise they wouldn't do it. Does that meaning apply to the rest of us? Is that meaning a function of truth? I think these questions are relevant.

"Mathematics is autonomous, and whatever you intend by 'meaning' that you so desperately want to find in mathematics is either not there, or if it is, it is to be found in the ordered totality of mathematics."

You imply that the debate about an autonomous mathematics is settled. There are many critics of this complacency. You suggest the place to discover the truth of the matter is to look at peer-reviewed journals. I suggest that's like expecting the foxes to keep watch over the chicken coup. Nevertheless, there are mathematician who have noted the issue is not settled -- and that it may get worse the further math ventures off into the purely abstract.

"but already in Euclid's elements' book, arguably the most important book in the history of mathematics, whatever connection to the actual world there is is blissfully ignored."

And I deny that. Euclid's postulates may have blissfully ignored a connection to the actual world but only because of blissful ignorance. This brings me to the question I posed above, where do you think Euclid got those ideas for postulates in the first place? Why did he assume they were true? How did they jump into his mind? Why is it hard for us to dispute them? IOW, what is self-evidence, really? I think experience has taught us from the day we were born. Experience has convinced us of fundamentals like: we can walk between any two points and we can keep on walking in that straight line. That just seems obvious because experience has given us every reason to trust that belief. By time we learn space may warp and non-Euclidean geometry may be valid too, it's too late.

I've been wanting to answer some of your items but have been short of time this week. I'm sure you'll be sad to hear I'll make time this weekend. But I've got to answer this:

"Note that I didn't even dispute your question-begging assertion that disputes with diverging differences of opinion find their truth-values from consensus, or convergence between the disputing parties."

I did not make that assertion. I don't believe truth is found through consensus -- it's not decided by vote. I do think people will gravitate towards a consensus if someone does discover a truth and makes a compelling case for it. Regardless of your paltry examples, it's clear that there is no consensus developing on a lot of purely "philosophic" issues. And it's clear consensus does eventually develop on scientific and empirically-based issues.

I could respond to your points but I will not. Respond to my two questions first. Why am I insisting on this? Because I want to get clear on what *you* mean by such words as "meaning" and "relevance" as regards mathematics. Otherwise, we will keep talking past each other.

In Philosophy of Mind Feser argues: "When we say that 'Smoke means fire,' we're not speaking literally." He doubts correlation is enough for a basis for meaning. He asserts the word "smoke" means smoke in a different way than "Smoke means fire." To Feser, this causal "meaning" doesn't explain why smoke means anything at all. The meaning of smoke (the cloud of particles) "has nothing to do with its causal connection to fire and everything to do with our powers of interpretation and evaluation of evidence."

Well, of course we interpret. Fire has correlated to smoke in my experience. That justifies an initial thought that there is likely fire. Our brains don't wait for certainty. They make judgments (and modify them) real-time. This, IMO, is fundamental for meaning. Meaning is the act of our brain searching through past experience and drawing conclusions about input based on best available evidence. Meaning is essentially a measurement of the probability that current input matches some combination of past input. Our brains scan for remembered patterns, close matches trigger what we then call meaning.

But let me elaborate. Smoke doesn't simply mean fire. It could mean my house is in danger, my life is in danger, a neighbor or pet is in danger. We might connect smoke to movies we've seen (Up in Smoke), songs we've heard (When Smoke Gets in Your Eyes) and even dates we were on when we heard those songs. Meaning depends on a network of memories that ripple throughout portions of our experience. So the claim that "Smoke means fire" is merely the first and most obvious connection in what ends up being dozens if not thousands of nearly immediate associations. Our brains act fast in narrowing the current (and tentative) meaning to the best fit for the immediate situation, but meaning goes much deeper than those first, most obvious associations. That, in a nutshell, is what I think meaning is.

So how does this relate to mathematics? I'll start with "apple." We see the word. The word is a key into our mental database. We associate the word with the colors of apples, sizes, textures, myths (Adam and Eve, Newton), deserts, Mom and America. There is no way we can prevent "apple" from triggering experiences we've had with apples and about apples. It happens automatically. Some of it happens unconsciously -- like our understanding that apples are very different from oranges. This is all part of the meaning of "apple." It's personal and it's part of us at the neural level.

Math and geometry are the same way. Numbers are something concrete to us. Long before any formal introduction to math, we are very familiar with the empirical fact that two objects are different than one object. Numbers are not detached concepts that float down by accident or are misunderstood until we learn algebra. We have put our hands on a number of things since before we could talk. The mere mention of numbers makes those connections to our lives and how we experience numbers of things. There is no way a mathematician can seriously argue he forgot that lifetime of experience. He cannot seriously argue those numbers had no meaning for him before he took a professional interest. I see no way around this basic experience with the universe.

"How can such an empiricist hold that there is no such thing as a necessary truth? This is the only world we can measure and observe, so anything true is true in this (ie, all) world(s)."

There may be only this one universe. I doubt we'll ever know another. But it doesn't follow that even given one universe only, it is a necessary one. Maybe our usage of necessary is different.

"Because to believe in possible alternatives 'rooted nowhere in material substances' would be to have 'an unreasonable faith' in theory over practical experience - far from the empirical evidence demanded of others."

I may need clarification on this. You seem to be saying I can't believe in other universes because I have no material evidence. Yeah, it's kind of true, I don't believe we can know anything about another universe one way or the other. So I don't see how we can pretend to know its nature and that a truth here must be a truth there.

Material evidence for the immaterial would be great. On this blog such a request shouldn't be unreasonable. Aquinas seems to believe we get indirect evidence of God this way. Nevertheless, and regardless of what you think, I'm willing to listen to compelling non-material evidence but I have no idea what that would be.

"'What is your evidence rooted somewhere in material substances for the claim that our universe isn't necessary, it simply is?' I'm not questioning its existence but how you know it's contingent, and not necessary."

I don't have evidence that it's either necessary or contingent. What if it's eternal? To me, an eternal thing just is. Then those two categories (necessary or contingent) don't seem to apply.

"To me, your statement (3) is materially different from saying 'I do not know whether this universe is necessary or not.'"

I don't know if it's necessary or not. I hope I did clarify that. I don't think it's an either/or category. It seems absurd to me to put an eternal thing into that category. I'm not one of those people who believes there *must* have been a creation. If there was no creation, I don't see how we could say it must have been created (that's absurd), or could have never been created (that's absurd). IMO, both categories presume a creation.

"I have to ask, therefore, of your statement (1): did you mean to say, 'I do not know if there are such things as necessary truths?'"

I didn't mean to say that but I have no problem rephrasing my statement to exactly as you wrote it. I do not know of a necessary truth. I don't know what form that would take. I don't know how we would distinguish between a necessary truth and a plain vanilla truth. Let's face it, plain vanilla truths are hard enough to find.

"Because if (1) stands, I still have a problem: it doesn't appear to be a statement about physics or matter so how did you evaluate its truth empirically?"

I'm not so sure. If all we know (that is, all that we are relatively sure is more true than untrue) is based on empirical evidence, and no empirical data appears to be necessarily true, and all other epistemological foundations seem to lead to unconvincing results (non-truths), it seems to follow that we observe no necessary truths. Now it doesn't follow that none will ever be found, but there is no good reason to give the possibility of "necessary truth" the benefit of the doubt.

"Also, given that there are no empirical observations you can make to determine the truth of your statement (2), ie, that the faith expressed there is 'rooted nowhere in material substances, could you explain what makes your faith in this case 'reasonable'?"

I'm not sure what you mean or think I mean here. Maybe I phrased it poorly. I do have faith that the universe exists and we are not brains in a jar or computer simulations. I frankly think people who believe such things are nutty -- far more nutty than all but a few theists. I also have faith that all our experience comes from within this material universe. If there is a mysterious second realm it appears to have no interaction -- and no possible way to interact -- with us (regardless of what Thomists assert). So if there is no interaction there can't be meaning if meaning is what I think it is (posted above). People claim this second realm exists but people claim all sorts of things. We cannot rationally believe in every claim people make. We can't rationally treat every claim as worthy and ignore the fact that many are bizarre. That blind credulity would be irrational.

"You say: 'It is possible that 2+2=5 is true somewhere but we can't wrap our heads around the 'weird physics' of such a world' - ok, how do you know this is true? Where did you physically observe this fact that 2+2=4 isn't necessarily so?"

-- that's a strange request of you. I don't know that there is a universe where 2+2=5. I never claimed to know. In fact, I claimed we cannot know. I claimed you have no empirical (or other) evidence that such place cannot exist. Of course none of us can demonstrate this empirically. I make no secret of my preference -- and insistence -- that truth be grounded somewhere in empirical evidence. But it simply does not follow that I am prevented from exposing faulty reasoning when reason itself can expose it. I do not deny reason and logic. I don't know why you would even make is sort of bogus claim against me. Reason is often used by empiricists to draw conclusions from physical evidence. And reason is used to expose fallacies coming from other directions. There is nothing contradictory or suspicious about this, just like there is nothing contradictory or suspicious when non-empiricists use empirical evidence to support their arguments.

"I imagine you have a problem with the series of numbers being infinite? But you should agree that there are only finitely many material things. So what happens, in your view, when you take the number of all material things and add 1 to it, or multiply it by 2?"

It can't be done. I know people say it can be done. They probably believe it can be done. But it cannot. We have a finite number of brain cells. Even if it were possible to allocate every brain cell to a really big number, there is a theoretical limit on how big a number we can grasp in our head. And that number would fall far short. And we cannot write it either. To write it implies we need something to write on. And nothing we can write on would ever be big enough. The only way we can express it is to use some abstract approximation -- like 1000 to the power of 1000 to the power of 1000. That's not the number. That has a severe rounding problem. It's a ballpark number, not the real thing.

But even if we could, there's still no problem. We can imagine lots of things both true and untrue. Imagining, or inability to imagine, has no effect on reality.

C.S. Lewis did not settle anything with his rewrite of his Argument from Reason. So there was no convergence of opinion. I don't claim individuals won't alter their opinions. I claim that in the vast scheme of things, philosophical and religious views diverge over time. Over time there are more and more unique opinions even on basic issues.

"(2) A formal proof to the theory of Pierre de Fermat's that no +ve integers a, b, and c can satisfy the the equation a^n + b^n = c^n for any integer value of n greater than two had been the subject of centuries of dispute till 1993."

You assume math has no foundation in the material world. I dispute that.

"...differences of opinion have not converged (eg. Global warming/climate change/climate disruption, and Darwin's theory of evolution among many)."

There is very much convergence regarding the Theory of Evolution. The hold-outs are (for the most part) religiously motivated and/or uninterested in the topic. As for "global warming," that's a recent issue and, as we learned, has much political motivation on both sides. Ultimately that issue will be settled one way or the other.

"I would also note, as an aside, that in the past you've been quick to impute intellectual dishonesty to your host here,"

Feser is quick to impute intellectual dishonesty on his opponents.

"Yet you ignore questions that you can't answer,"

If I miss something it's either because of time or I thought other issues were more important.

"if you were consistent you would have to say 'I do not know about x as I have no material evidence for it.'"

For example...?

"I'd love for you to have access to all the tools of philosophy to make your case. But, given that you reject them..."

You've clarified much, but I still think we're speaking past each to no small degree - particularly in what it means to be necessarily true.

I don't think there's much value in re-heating it. But I do find it remarkable that you believe math, which takes as its starting points pure abstractions (ie, conceptual premises in the way of axioms and postulates) and from them reasons to necessary conclusions, is founded in the material; and yet you dismiss metaphysical conclusions for the existence of the immaterial even though its arguments start from empirical premises.

Also you do deny reason and logic if you insist that the absence of material evidence for reasoned and logical conclusions invalidate those conclusions. You just don't deny reason and logic consistently, engaging them when you feel they help you.

Is there a reason why you keep dodging my two very simple questions? I have already told you, if you answer my two questions, my answer to your philosophy of (anti-)mathematics will be very much facilitated

I am sorry if I missed your answers. I have just reread your response and cannot find it anywhere. Here goes again:

Let us imagine that we lived in a universe where Euclidean geometry had absolutely no relevance whatsoever to our empirical theories. How would you characterize a mathematical work expounding it (e.g. a version of Euclid's elements)? Is it "meaningful"? If not, why so? Is it "relevant"? If not, why so?

Djindra:You didn't so much argue for, as assert, your material basis of math. You're wrong, but I note your formulation now is "real world experience".

As I mentioned before, the metaphysical arguments that you deride take empirical premises as their starting points.

Now here's where you get extremely confusing. You claim that you don't deny logic, even as you qualify that logic alone is insufficient to reach reliable conclusions. Now if you accept the premises of an argument and the deductive reasoning commits no logical fallacies you are bound to accept its conclusions, ie. the conclusion follows necessarily. That is logic. If you don't accept that, you deny it - no qualifiers needed.

The supremely smart TheOFloinn has pointed out elsewhere that there is no empirical proof that the ratio of a circle's circumference to its radius is an irrational number.

Is this a finding of math that you reject? If so the deeply persistent weirdness of your materialism/nominalism/whatever has another data point. If not then: real world experience + deductive reasoning = what you have in the metaphysical arguments you deride. Rejecting one (metaphysics) and not the other (math) seems arbitrary - frankly, it's all prior commitment and faith based. Strange that you should aim that accusation at everyone but yourself.

"Let us imagine that we lived in a universe where Euclidean geometry had absolutely no relevance whatsoever to our empirical theories. How would you characterize a mathematical work expounding it (e.g. a version of Euclid's elements)? Is it "meaningful"? If not, why so? Is it "relevant"? If not, why so?"

In that imaginary universe, Euclid's elements would have the meaning of a Jackson Pollock painting. That is, the meaning would be non-existent for most. For those few who claimed meaning it would be meaning of a totally subjective nature. It would be totally subjective because the geometry would have, at best, a trivial relation to the real world.

For the purposes of a discussion on nominalism vs realism this sort of meaning poses no problem. I know you aren't specifically interested in that dispute but I am.

Btw, I ran across Alfred Rényi's "A Socratic Dialogue on Mathematics.'' He put some words into Socrates that are very similar to what I've been saying:

SOCRATES: "Let us recall how the abstract concepts of mathematics developed. We said that the mathematician deals with pure numbers, and not with the numbers of real objects. But do you think that somebody who has never counted real objects can understand the abstract notion of number? When a child learns counting, he first counts pebbles and small sticks. Only if he knows that two pebbles and three pebbles make five pebbles, and the same about sticks or coins, is he able to understand that two and three make five. The situation is essentially the same with geometry. The child arrives at the notion of a sphere through experiences with round objects like balls. Mankind developed all fundamental notions of mathematics in a similar way. These notions are crystallized from a knowledge of the real world, and thus it is not surprising but quite natural that they bear the marks of their origin, as children do of their parents. And exactly as children when they grow up become the supporters of their parents, so any branch of mathematics, if it is sufficiently developed, becomes a useful tool in exploring the real world."

"In that imaginary universe, Euclid's elements would have the meaning of a Jackson Pollock painting. That is, the meaning would be non-existent for most. For those few who claimed meaning it would be meaning of a totally subjective nature. It would be totally subjective because the geometry would have, at best, a trivial relation to the real world."

The appeal to the majority in "the meaning would be non-existent for most" is irrelevant, as already in this, our universe, there are plenty of things (quantum mechanics, say) that have no meaning for most people. As far "For those few who claimed meaning it would be meaning of a totally subjective nature." either it is a meaningless sentence (I won't even go into your statement about art and subjectivity), or I have to congratulate you, as you have just consigned vast swaths of mathematics to the dust bin and in the process, hampered the progress of *all* disciplines that depend on it including physics and chemistry, that is, our most fundamental empirical sciences.

Look, let me see if I can get you to understand this simple fact. It is clear to everybody that a great many mathematical concepts were borne out of very practical needs: numbers and Euclidean geometry are the most obvious examples. This much is obvious and I have already said so in previous posts. The point is not that there are mathematical concepts that were borne out of experience, the point is that there *ARE* mathematical concepts that were *NOT* borne out of experience with the real world, but a different sort of experience, of the mathematical variety. Do you think that topologies, Banach spaces, sheaves, derived categories, cohomology theories (and the list could go on indefinitely) were devised by staring hard at reality? No, instead they were devised as an answer to natural *mathematical* questions, to solve *mathematical* problems. They are not the random concepts of minds with nothing better to think about, rather they are the product of the organic development of mathematics. Their meaningfulness, their relevance, is judged by the relative position they occupy in the total order of mathematics. In turn, these concepts generate new mathematical questions that need to be answered. They have also found their way into other disciplines such as physics, but there is nothing mysterious or magical about this, since in the measure that a discipline is able to frame its questions in a mathematical language, then almost of necessity it will get hold of the tools that mathematicians have developed. That you, or any other ignorant, finds these concepts meaningless is absolutely irrelevant.

And this is the true test of what constitutes an autonomous discipline: it has its own conceptual framework, it generates its own questions, its own tools. It may come into a dialogue with other disciplines, as mathematics surely does, but it retains its independence in the sense that it has its own framework, its own standards of value not borrowed ready-made from any neighboring disciplines.

All I have made are rather banal observations. It is irrelevant if you espouse some specific philosophy of mathematics (or even none for that matter). To stress once again, these are facts. But by all means, feel free to ignore the facts and hold onto your ignorance-driven beliefs.

"you have just consigned vast swaths of mathematics to the dust bin and in the process, hampered the progress of 'all' disciplines that depend on it including physics and chemistry, that is, our most fundamental empirical sciences."

No, I have not. You presume I think mathematics is subjective. I do not. Nor do I assume you think it is. Our dispute is not over that question. It's over the reason math is, or can be, objective. You seem to think this objectivity can drop out of the sky with no strings attached. I say that is not objectivity. That's blatant subjectivity.

We both agree mathematical concepts should not be considered "random concepts of minds." But why aren't they? I say they aren't because their foundation is solidly in the empirical world. I think you have essentially agreed but then seem to think that the further we get from the foundation the less important it is. I disagree on that.

"the point is that there *ARE* mathematical concepts that were *NOT* borne out of experience with the real world, but a different sort of experience, of the mathematical variety."

No matter how hard you try, you cannot unhinge derived truths from its solid foundation.

"Do you think that topologies, Banach spaces, sheaves, derived categories, cohomology theories (and the list could go on indefinitely) were devised by staring hard at reality?"

How do you know they are true? 1) The theory must match up (model) in some way with empirical data, or 2) The foundation is based on empirical data. Without either of these we cannot reliably argue a statement is true. No matter how well it worked out on paper, non-Euclidean geometry was little more than a curiosity prior to Einstein's Relativity. We have conflicting geometries, Euclidean and non-Euclidian. These geometries may appear to be mathematically correct. But which is absolutely true? How do we decide? Maybe we should think of math as no more than a handy tool. Application to the real world is the only thing that lends "truth" to it. It doesn't actually possess it at all. It models it. It mimics it.

"Their meaningfulness, their relevance, is judged by the relative position they occupy in the total order of mathematics."

And that totality includes the empirical foundation.

"That you, or any other ignorant, finds these concepts meaningless is absolutely irrelevant."

That you, or any other ignorant, finds foundations useless is absolutely irrelevant.

"And this is the true test of what constitutes an autonomous discipline: it has its own conceptual framework, it generates its own questions, its own tools."

And mathematics fails this test. It depends on its empirical foundation. You too are free to ignore that fact and hold onto your ignorance-driven beliefs.

"How do you know they are true? 1) The theory must match up (model) in some way with empirical data, or 2) The foundation is based on empirical data. Without either of these we cannot reliably argue a statement is true. No matter how well it worked out on paper, non-Euclidean geometry was little more than a curiosity prior to Einstein's Relativity. We have conflicting geometries, Euclidean and non-Euclidian. These geometries may appear to be mathematically correct. But which is absolutely true? How do we decide? Maybe we should think of math as no more than a handy tool. Application to the real world is the only thing that lends "truth" to it. It doesn't actually possess it at all. It models it. It mimics it."

The above passage says it all; you simply do not know what you are talking about. Feel free to ignore the facts, feel free to call me ignorant (it is ironic that you are ignorant of mathematics and yet pontificate about its foundations with absolute certainty), I really do not care. By this point, you are a hopeless, wilful ignorant. As Dr. Johnson said, I found you an argument, I am not under the obligation to find you an understanding.

You're just blowing smoke. I am not ignorant of mathematics. I grew up counting like everyone else. I'm very familiar with software. We might think of mathematics as a subset of my profession. It's you who has shown you have no understanding of the issue.

I find that the statement God creates something out of "nothing" can cause confusion. Nothing cannot come from nothing (as in sheer nothingness).

What I am trying to say is, shouldn't the argument be that God create something out of his existence of pure actuality rather than phrasing it as if something can actually be created from "nothing"? God isn't nothing so he is not literally creating "out of nothing".

I THINK the problem is people like to show off their supposed awesomeness, clouding things, more than actually seeking to strip things down bare.(I speak of the comments not the author)

Every night we all create entire worlds with our Thought. So we have a clear example of creation from nothing every night.

One professor once said to me-- God doesn't have to kill you--he could simply stop thinking of you.

Now we dont have god like powers in our dreams--we cant give the people independent thought but God has given us all a place in his mind. To think of this physical world as somehow separate from God's thought is just so feeble a concept. There simply is no "place" for God to put us. He is the only one who truly exists so all of creation must be In Him.

He is life and has shared that with us. Designing worlds from Thought alone. Substance is just OUR perception. We are real because God says we are real.

About Me

I am a writer and philosopher living in Los Angeles. I teach philosophy at Pasadena City College. My primary academic research interests are in the philosophy of mind, moral and political philosophy, and philosophy of religion. I also write on politics, from a conservative point of view; and on religion, from a traditional Roman Catholic perspective.